Here I write about things that may aid those who are new to Signal Processing to grasp a few concepts without necessarily referring to a textbook.
The table below shows some the differences between a Wave and a Wavelet.
Essentially a Wavelet is a small wave with pretty much the opposite characteristics to that of a wave. This is exactly what makes their application appealing to time variant signals such as stock prices. Accompanying wavelets is the Wavelet transform algorithm, of which there are many variants, but all essentially do the same thing using different ways. The table below shows the difference between two contrasting analytical algorithms.
So what are these “domains” we are referring to? Any signal that is a function of time is in the time domain. Stock prices are in the time domain because the each point in time has a price associated with it. Now consider another time domain signal such as a sine wave. Lets assume that this signal has amplitude 2 and takes 5 seconds before it begins to repeat itself i.e. it’s period is 5 seconds. Now the frequency of this signal is the inverse of the period which is 0.2 hertz in our case. Also the amplitude of the signal is the in the frequency domain our sine wave will look like a single spike of height 2 at the point 0.2 hertz. This is because the frequency domain shows the amplitude or power of the signal (y-axis) for different frequencies (x-axis), which is referred to as the spectrum. The spectrum of a stock price takes a more complicated form and is more difficult to determine, but the wavelet transform takes care of that.
Now it is worth pointing out that wavelets are usually combined with other signal processing algorithms to form “systems” that enable the transformation from the time domain into the frequency domain to happen in particular ways, depending on what you want to achieve. For instance instead of determining the spectrum of the stock price one may want to develop a filtering scheme or a trend/cycle estimation scheme. We shall see more of that later.
